Question

The graph below shows the relationship between the number of months different students practiced boxing and the number of matches they won:

The title of the graph is Boxing Matches. On x axis, the label is Number of Months of Practice. On y axis, the label is Number of Matches Won. The scale on the y axis is from 0 to 21 at increments of 3, and the scale on the x axis is from 0 to 12 at increments of 2. The points plotted on the graph are the ordered pairs 0, 3 and 1, 6 and 2, 7 and 3, 9 and 4, 11 and 5, 13 and 6, 14 and 7, 16 and 8, 17 and 9, 18 and 10,20. A straight line is drawn joining the ordered pairs 0, 4 and 2, 7.1 and 4, 11 and 6, 13.5 and 8, 17 and 10, 20.5.

Part A: What is the approximate y-intercept of the line of best fit and what does it represent? (5 points)

Part B: Write the equation for the line of best fit in the slope-intercept form and use it to predict the number of matches that could be won after 13 months of practice. Show your work and include the points used to calculate the slope. (5 points)

Answer 1

(a) y intercept is approximately 4.3

(b)
`y = 1.5x+4.5`

Explanation:

Given

See attachment for graph

Solving (a) The y intercept

This is the point where
`x =0`

From the attached graph; By observation

`y \approx 4.3` when
`x =0`

So, the y intercept is approximately 4.3

Solving (b): The equation of best fit.

First, calculate the slope of the line using:

`m = (y_2 - y_1)/(x_2 - x_1)`

Where

`(x_1,y_1) = (9,18)`

`(x_2,y_2) = (8,16.5)`

So:

`m = (16.5- 18)/(8 - 9)`

`m = (-1.5)/(- 1)`

`m = 1.5`

The equation is then calculated using:

`y =m(x - x_1) + y_1`

Where:
`m = 1.5` and
`(x_1,y_1) = (9,18)`

`y = 1.5(x - 9) + 18`

`y = 1.5x - 9*1.5 + 18`

`y = 1.5x - 13.5 + 18`

`y = 1.5x+4.5`